My research interests lie in symplectic and contact topology, algebraic and differential geometry, and mathematical physics. My current work focuses on invariants of Legendrian and Lagrangian submanifolds arising from the microlocal theory of sheaves, with particular emphasis on categorical and sheaf-theoretic approaches to Legendrian link invariants and braid varieties. Looking ahead, I aim to investigate connections with Floer-theoretic constructions, as well as their applications to the categorification of braid varieties and to geometric problems such as the study of exact Lagrangian fillings.
More broadly, I am interested in interactions between symplectic geometry and mathematical physics, including the study of classical field theories with boundaries from a geometric, covariant Hamiltonian perspective.
I am always happy to discuss potential collaborations and new research directions.
A. Rodríguez–López, Computable sheaf invariants for Legendrian rainbow closures, arXiv:2511.15078 [math.SG], 2025, 156 pages.
J. Berra–Montiel, A. Molgado, and A. Rodríguez–López, A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity, Class. Quantum Grav. 38, 135012 (2021), arXiv:2101.08960 [gr-qc].
A. Molgado and A. Rodríguez–López, Covariant momentum map for non-Abelian topological BF field theory, Class. Quantum Grav. 36, 245003 (2019), arXiv:1907.01152 [gr-qc].
J. Berra–Montiel, A. Molgado, and A. Rodríguez–López, Polysymplectic formulation for BF gravity with Immirzi parameter, Class. Quantum Grav. 36, 115003 (2019), arXiv:1901.11532 [gr-qc].